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題 名 | The Variational Equations for Coupled Rigid Bodies System: A Case Study in Modeling of a Two-DOF Rotational Mechanism=應用變分方程式建構耦合剛體系統之動力模型 |
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作 者 | 蔡樸生; 吳德豐; 陳珍源; | 書刊名 | 中華技術學院學報 |
卷 期 | 25 2002.09[民91.09] |
頁 次 | 頁165-177 |
分類號 | 448.51 |
關鍵詞 | 運動方程式; 變分方程式; 約束機械系統; 耦合剛體系統; 機械人操作器; Equations of motion; Variational equations; Constrained mechanics; Coupled rigid bodies system; Robotic manipulator; |
語 文 | 英文(English) |
中文摘要 | 基於變分方程式的原理,本文提出一個新的理論架構,針對複雜的耦合剛體系統建立其動力模型。變分描述了受約束系統之自由度,並提供了一個自然的觀點來敘述不同的力學原理,以便進一步分析系統之複雜動態行為。變分方程式的建模程序是以古典力學的達朗貝原理作出發,本文所提出的方法除了架構系統的動力方程式之外,對於最後的模型也提出一套以拉格蘭濟原理為基礎的驗證法則。利用變分法進行動力方程式的推導具有以下特點:(1)推導過程最具系統化與結構化,故計算方便。(2)方程式可處理N個剛體,故可適用與推導多體運動之動力方程式。(3)完整約束與非完整約束具有一套共同處理模式,使得約束方程式在很自然的情況下引入系統動力方程式中,省掉拉格蘭濟乘積因子之困擾。(4)使用模組化的推導過程,我們更能夠掌握每一條約束動力方程式的幾何與物理意義。最後,我們以一個兩自由度的旋轉機構為例,嘗試推導它的動力模型並驗證其結果,顯示本文所提的變分建模程序之優越性。 |
英文摘要 | Based on the variational equations of mechanics, a new modeling scheme for the dynamics of the coupled rigid bodies system (CRBS) is proposed in this paper. A derivation model procedure will be construed as the preliminary of classical mechanics is introduced. This scheme consists of two parts: one is to obtain the dynamic model of the CRBS by use of the variational equations, and the other is to confirm the validity of this model by means of Lagrange mechanics. The main idea of this scheme follows the powerful ability of the variational equations to model the dynamics of the CRBS in a systematical manner. No matter how coupled the rigid bodies system is, the dynamics is always obtained by following the proposed procedure. Furthermore, it is easy to develop a program to implement the proposed scheme such that modeling a complex CRBS becomes conveniently. Finally, in order to demonstrate the advantages of our scheme, the dynamics of a two degree-of-freedom (DOF) rotational manipulator, often used as the attitude control mechanism, is derived by following the proposed scheme. |
本系統中英文摘要資訊取自各篇刊載內容。